1,296 reputation
613
bio website math.univ-toulouse.fr/…
location Toulouse
age 43
visits member for 2 years, 8 months
seen 2 days ago
Chercheur au CNRS, working in Toulouse. I don't usually comment or answer questions from anonymous users.

Apr
1
comment Are there perverse sheaves on abelian varieties with small Euler characteristic?
Isn't $d=g$ in your last statement ?
Apr
1
comment Is it possible to prove Mordell's conjecture geometrically?
This is a good question. It has always struck me that the only known proofs of the Mordell conjecture over number fields, as well as of the Manin-Mumford conjecture require arithmetic models. The only thing I know in the "purely complex" (or "geometrical") direction is Zannier-Pila's approach to Manin-Mumford (but not Mordell...), which still requires arithmetics, but less so than Raynaud's (or Ullmo-Szpiro-Zhang, or Pink-R.'s).
Mar
23
comment Chow ring of a $\mu_2$-gerbe
I have only recently come across your question. Do you actually mean a $\mu_2$-torsor ?
Mar
23
comment Inequality regarding sum of gaussian on lattices
It might be interesting to consider the special case where the lattice comes from the fractional ideal of a number field. Then you could use the functional equation of the theta function. See arxiv.org/pdf/math/9802121v3.pdf or math.univ-toulouse.fr/~rossler/mypage/pdf-files/…
Mar
21
comment A naive algebraic geometry question
See Hartshorne, Ex. III.4.2, p. 222 (Chevalley's theorem).
Mar
12
comment Chow ring of two varieties
This is true for varieties having an 'algebraic cellular decomposition'. See Example 19.1.11 in Fulton, Intersection Theory, p. 378.
Mar
12
comment Given a morphism of schemes, when does bijective + isomorphic tangent spaces = isomorphism?
See Lemma 2.4, p. 172 in Cornell-Silverman, 'Arithmetic Geometry' (article by Milne) for a statement in the direction of what you are looking for.
Mar
11
comment Chow ring of two varieties
About this, see Ex. IV.4.10 in Hartshorne.
Mar
9
comment Formal completion of the normal bundle
I think you need to complete the symmetric algebra along the augmentation ideal to get the iso. of $k$-algebras you mention.
Mar
8
comment Formal completion of the normal bundle
@Will Savin: PS: The OP considers the formalisation of $Z$ inside $N_{Z/X}$, not the formalisation of $N_{Z/X}$ (unless I have been completely mislead).
Mar
8
comment Formal completion of the normal bundle
@Will Savin: what do you mean by 'the completion is a bundle' ?
Mar
8
comment Formal completion of the normal bundle
PS The above is only valid in char. 0 because it uses the exponential map.
Mar
8
comment Formal completion of the normal bundle
Suppose for a moment that the ideal $Z$ is generated by an element, which is not a zero divisor and that $Z$ is smooth over the base field. Then Lemma 3.6 in 'Differential algebra - a scheme theory approach' by H. Gillet will prove that the answer is yes. Note that the isomorphism depends on the choice of a derivation. The general case (if $Z$ is smooth) should be provable along the same lines. For a general schematic regular immersion, I think this still works, if you can produce the relevant derivations (my guess is: if the normal bundle is trivial).
Mar
5
comment Log forms and Tate classes
If $X$ is proper over $\bf C$ then any such $f_i$ would be constant. But maybe you mean that the expression is local ?
Mar
5
comment Degeneration of the Hodge spectral sequence for scheme over truncated Witt ring?
Actually, I don't know such counterexamples. The only ones I know are the classical ones (ie those mentioned at the end of the article of Deligne-Illusie).
Mar
4
comment Degeneration of the Hodge spectral sequence for scheme over truncated Witt ring?
... But if you require the Frobenius itself to lift to $W_2(k)$, then the curve has to be ordinary. See for instance Prop. 8.6 in 'Frobenius et dégénérescence de Hodge' by L. Illusie (this is also a result of Nakkajima).
Mar
4
comment Degeneration of the Hodge spectral sequence for scheme over truncated Witt ring?
In Berthelot-Ogus, it is supposed that the Frobenius lifts to an entire formal lifting, which is a stronger hypothesis. Nevertheless, the proof of Th. 8.8 in Berthelot-Ogus does not depend on the whole strength of this hypothesis, I think (that is why I wrote 'essentially'). As far as supersingular elliptic curves are concerned, the result of Deuring shows that the curve lifts to a CM curve and therefore a certain power of Frobenius lifts (if $k$ is a finite field). Nevertheless, the lifting will in general be defined over a ramified extension, unlike here. ...
Mar
4
comment Degeneration of the Hodge spectral sequence for scheme over truncated Witt ring?
To put a condition on Frobenius lift is too strong. For instance, it forces ordinarity. Also I think that the result you are referring to is basically already in Th. 8.8 of the notes of Berthelot-Ogus on crystalline cohomology.
Feb
27
comment Degeneration of the Hodge spectral sequence for scheme over truncated Witt ring?
There is something in this direction in the paper by Deligne-Illusie: see eq. (2.2.1) p. 254 in their paper in Invent. Math. 89.
Feb
25
comment Whether the multiplicity changes under a fields extension
What is the 'original image of $\xi$ in $X\times_k X$' ?